Tying Social Security cost-of-living increases to the 'chained' CPI is a foolish way to tackle the deficit — a goal that itself has been revealed to be largely based on erroneous research.

Washington's tug of war over the federal budget has many wonders, but the biggest one of all must be the lengths to which politicians and pundits will go to deprive Granny and Grandpa of $30 a month.

That's the amount by which benefits for the average Social Security retiree would be reduced by 2023 under a provision in President Obama's new budget. It might not sound like much to the president or fans of the proposal in both parties and the Washington commentariat. For the retiree trying to stretch an average monthly check of about $1,200 to cover housing, healthcare and every other necessity under the sun, it looms rather larger.

The idea that Social Security benefits should be on the table in budget talks arises from the fear that America's national debt, driven by its budget deficit, is growing to the point that it will push us over the economic brink.

Here's the tragedy of it: That fear is based on junk economics.

Many economists knew that already, but it has been underscored by the exposure of material errors in a widely circulated academic paper that provided an intellectual foundation for the idea that the federal debt was getting so far out of control that only dramatic cuts in spending could save us from the abyss.

The paper, published in 2010 by economists Kenneth Rogoff and Carmen Reinhart, postulated that economic growth falls off sharply once a country's debt exceeds 90% of its gross domestic product. The finding packed a lot of punch at the time because U.S. debt was approaching that range.

It would be inaccurate to say the paper inspired the deficit panic and austerity politics that we've lived with ever since, but it certainly provided deficit hawks with what seemed to be empirical data to support their alarm.

But as documented by a graduate student and two professors at the University of Massachusetts, the Rogoff/Reinhart paper was riddled with mistakes. These were a spreadsheet coding error that left five countries out of their sample of 20 out of their calculations, "unconventional weighting" of their country statistics in a way that bolstered their thesis, and the "selective omissions" of several countries and years from their overall analysis.

In replying to the critique, Rogoff and Reinhart copped to the first error, defended the second as a reasonable weighting, and indignantly denied that they had deliberately selected their data; the reason for the omissions was that the data were unavailable when they wrote the paper, they said.

They also observed that the UMass team agreed with their finding that higher debt is associated with lower economic growth. But that glosses over two leading criticisms of their paper — that it suggested that economic growth all but falls off a cliff at the 90% threshold, and that it didn't consider that high debt might be caused by low growth, rather than the other way around.

The latter point is especially important, because it points to very different policy prescriptions depending on which way the causal merry-go-round spins. Those citing Rogoff and Reinhart have argued invariably that it means America must cut its debt load urgently.

That's a big edifice to erect on a debunked economic paper. But it brings us back to Obama's budget, which seems preoccupied with deficit reduction — he alluded to the concept 17 times in his April 10 budget message.

Front and center among his proposed deficit-reduction tools were changes to Medicare and Social Security. The former involved increasing premiums paid by higher-income seniors. The centerpiece of his Social Security rollback was a change in the index for cost-of-living increases from the traditional consumer price index to the "chained" CPI.

If you've been following the Washington debate, you know that the uncanny popularity of the chained CPI as a deficit nostrum lies in its supposed "accuracy." The idea is that it incorporates certain changes people make in their purchasing behavior when prices rise — when apples go up in price, they buy bananas instead. Therefore it typically yields a lower inflation number.

What you may not know is that these behavioral changes are very hard to track and the conclusions applied by the index-makers often conjectural. (What if you like apples but not bananas?) Experts also debate whether consumers respond to absolute price changes or relative price changes — if hamburger is cheaper than steak but its price rises faster, people may actually buy more steak. And under many circumstances people may not have a choice: If gasoline goes up, you may not have the option to take the bus to work instead.